If f ( x ) = ( a x + b ) ( x 5 </msup> + 1 ) &#x2212;<

Pitrellais

Pitrellais

Answered question

2022-05-20

If f ( x ) = ( a x + b ) ( x 5 + 1 ) 5 x 1 is divisible by x 2 + 1 . Then the value of 2 a + 3 b

Answer & Explanation

szilincsifs

szilincsifs

Beginner2022-05-21Added 15 answers

We have
a x 6 + b x 5 + x ( a 5 ) + ( b 1 ) = P ( x ) ( x 2 + 1 ) + m x + n { m i + n = a + b i + i ( a 5 ) + ( b 1 ) m i + n = a b i i ( a 5 ) + ( b 1 ) { n = 2 ( b 1 ) 2 a 2 = b a 1 m = 2 b i + 2 i ( a 5 ) 2 i = a + b 5 { n = 0 , b a = 1 m = 0 , a + b = 5     a = 2 , b = 3     2 a + 3 b = 13.

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